a mistake in a 1990 paper

As we were working on the Handbook of mixture analysis with Sylvia Früwirth-Schnatter and Gilles Celeux today, near Saint-Germain des Près, I realised that there was a mistake in our 1990 mixture paper with Jean Diebolt [published in 1994], in that when we are proposing to use improper “Jeffreys” priors under the restriction that no component of the Gaussian mixture is “empty”, meaning that there are at least two observations generated from each component, the likelihood needs to be renormalised to be a density for the sample. This normalisation constant only depends on the weights of the mixture, which means that, when simulating from the full conditional distribution of the weights, there should be an extra-acceptance step to account for this correction. Of course, the term is essentially equal to one for a large enough sample but this remains a mistake nonetheless! It is funny that it remained undetected for so long in my most cited paper. Checking on Larry’s 1999 paper exploring the idea of excluding terms from the likelihood to allow for improper priors, I did not spot him using a correction either.